1.4 Summary
In this chapter, we have learned what vectors are and why we must use them in data science and machine learning. Vectors are not just a bunch of numbers bundled together but a mathematical structure that allows us to reason about data more effectively, both in theory and in practice. Contrary to popular belief, vectors are vectors not because they have direction and magnitude but because you can add them together.
This is formalized by the concept of vector spaces, providing the mathematical framework for our studies. Vector spaces are best described by bases, that is, minimal and linearly independent generating sets. Understanding vector spaces and their bases will pay enormous dividends when we study linear transformations, the most important building block of predictive models.
Besides the leap of abstraction provided by vectors, we reap significant benefits in practice by vectorizing our code, compressing complex logic into one-liners such as data scaling:
X_scaled ...
